Aquatic particulate absorption coefficient combining extraction and bleaching optimized for inland waters

The particulate absorption coefficient is one of the fundamental inherent optical properties describing interactions of light with material in water. Its spectral properties contain important information about chemical and biological constituents. It is often partitioned into algal and non‐algal fractions which provide useful information describing phytoplankton. Particulate absorption coefficient has been routinely measured in the ocean particularly to calibrate remote sensing algorithms. However, the methods to measure marine algal and non‐algal absorbing fractions might fail in freshwaters due to difficulties extracting green‐algae pigments and cyanobacterial phycocyanin and the high organic content of the non‐algal particles, making direct bleaching biased. In this work, we describe a method with sequential extraction, bleaching, and post‐processing to obtain unbiased pigments and non‐algal absorption fractions in freshwater environments, and we compare it against the resulting fractions obtained by only extraction or bleaching, using samples collected from 649 lakes across Canada. The resulting non‐algal particles spectra from our method appear free of interfering pigments while maintaining spectral shapes, as verified by the higher correlation coefficient between the 400 and 700 nm exponential coefficient (S, often referred to as slope) of the non‐algal particles spectra and the organic fraction of total suspended solids, and by having a better correlation between the ratio of absorption coefficient of phytoplankton at 620 and 676 nm and cyanobacterial biomass percentage. Overall, this method solves the two problems in freshwater particulate absorption partitioning associated with (1) unextracted pigments with methanol extraction methods and (2) bias introduced to non‐algal absorption spectra from NaOH bleaching.

by remote sensing, and its optical properties provide information about phytoplankton composition (Hoepffner and Sathyendranath 1993), particulate matter transport in coastal waters (D'Sa et al. 2007;Bélanger et al. 2013) and is a fundamental cause of underwater light extinction affecting major biogeochemical processes (Kirk 1980;Babin et al. 2003). Its separation into its components of algal particles (a φ , m À1 ) and non-algal particles (a NAP , m À1 ) is a key starting point to understand the bio-optical characteristics of lakes and the links to phytoplankton composition. However, while this separation is easily achieved in most seawater samples (Kishino et al. 1985;Bricaud et al. 1995), freshwater phytoplankton assemblages and pigmentation make this separation difficult (Tassan and Ferrari 1995).
The main basis for fractioning particulate absorption in marine and coastal water has been methanol extraction (Kishino et al. 1985): following soaking in methanol of the particulate matter collected on filters, the algal pigments are solubilized in the methanol solution while the non-algal particulate (NAP) remains on the filter (a E NAP , m À1 , where the superscript "E" refers to the methanol extraction). The difference between the absorbance measured of the filter before extraction, which represent a p , and after extraction provides the absorption coefficient of phytoplankton pigments in vivo (a E φ m À1 ). However, phycobilins and pigments of some chlorophytes are poorly extracted with this approach (Bricaud and Stramski 1990;Ferrari and Tassan 1999). For example, up to 13% of a φ 680 ð Þ remain unextracted in samples from reservoirs of the Neuse River basin in North Carolina (Vaehaetalo et al. 2005). Since phycobilins-containing phytoplanktonmostly cyanobacteria and cryptomonads (Becker et al. 2002;Seppälä et al. 2005)-are often an important fraction of the total biomass in lakes (Chow-Fraser et al. 1994;Reynolds 1997), methanol extraction has limited applicability in inland waters (Binding et al. 2008). An alternative to methanol extraction was developed to address these unextractable pigments, by treating the filters with sodium hypochlorite (NaOCl) (Tassan and Ferrari 1995;Ferrari and Tassan 1999). This procedure achieves complete depigmentation of the algal fraction by chemical oxidation of the light absorbing structures of organic molecules; however, some or all of the absorption of the NAP (particularly the organic fraction) will be lost or modified too (see Fig. 1A, top panel, yellow line; Binding et al. 2008). Other oxidations techniques also produce similar changes in a NAP (Estapa et al. 2012). A selective filter pad depigmentation using β-cyclocitral that bleaches chlorophylls and carotenoids but not the phycobiliproteins has been successful (Simis and Kauko 2012) but the effects on natural samples and a NAP has not been studied yet. Another method described by Simis et al. (2005) used a hot ethanol double extraction that left no trace of unextracted phycobilins in the non-algal fraction but did not extract all chlorophylls. In those cases, a NAP was substituted for an exponential fitted to the post-extraction filter a p spectra, which provides a NAP values with little bias, but some of the a NAP spectral shape can be lost if a NAP does not follow an exponential shape. This can happen when samples contain high concentrations of iron oxides terrigenous dust (Stramski et al. 2007), which are abundant in some inland waters, and in other coastal waters with high iron sediment loads (Estapa et al. 2012). Roesler and Perry (1995) removed the phycobilins with hot water after a hot methanol extraction in marine samples. The most recent International Ocean Colour Coordinating Group (IOCCG) reviews these and other methods for fractioning but they acknowledge that methanol extraction remains the most widely used in ocean science because it effectively removes most algal pigments in most environments (IOCCG Protocol Series 2018). For upcoming hyperspectral remote sensing platforms, maintaining all the spectral signatures as unbiased as possible is key for developing algorithms that can exploit the small nmlevel variations in the spectra (Giardino et al. 2014), potentially allowing even the determination of phytoplankton community composition (Xi et al. 2015;Zheng and DiGiacomo 2018;Reynolds and Stramski 2019). In this work, we describe a new approach of sequential methanol extraction and NaOCl bleaching that retrieves the NAP and algal fractions which, after appropriate fitting procedures, avoids most of the biases introduced by these methods separately. Fig. 1. Schematics of the steps used in the method proposed with synthetic spectra magnifying the spectral shape changes. (A) Limitations addressed by this work. Top: extraction (red) and bleaching (yellow) introduce biases to the fractioning of particulate material into its pigment and non-pigment (dotted) fractions. Bottom: Numerical processing methods such as exponential fit (heavy line) introduce additional biases to fractions estimation. (B) Methods compared in this work. Spectra are separated by source, as (direct) measurements, derived primary spectra (obtained as difference between two measured spectra) and secondary processing spectra (obtained from further numerical processing). The x-axis label textbox color differentiates the end products of each method. Red: extraction method (V1); yellow: bleaching method (V2); magenta: combined method proposed (V3). The numbers 1-4 indicate intermediate processing steps of the proposed procedure: (1) unextracted, bleached colored material; (2) isolation and of unextracted Chl a absorption (green background); (3) isolation of unextracted phycobilins absorption (blue background); (4) removal of isolated unextracted pigments from a NAP . (C) Absorption components of the three methods tested in this work.

Materials and procedures
Chlorophyll a concentration Chlorophyll a (Chl a) samples were obtained by filtration on GF/F from the same water sample as the absorption and measured both by fluorometry (two duplicates per lake; Mac-Intyre and Cullen 2005) and high-performance liquid chromatography (HPLC, one measurement per lake; Vinebrooke and Leavitt 1999). The chlorophyll measurements were averaged to obtain a three-replicate average. This was justifiable due to HPLC and fluorometry high collinearity (log-log type II major axis regression slope: 1.044 AE 0.036, intercept À0.369 AE 0.046, Pearson's R = 0.918) and close magnitude: fluorometry duplicates A and B root mean square percent error was 33.4%, while between HPLC and the mean of the fluorometry duplicates was 56.7%. The potential effect of chlorophyll b (Chl b) affecting the fluorometry measured was confirmed to not be present (as expected by the fluorescence protocol used, Welschmeyer 1994) after comparing the correlation of the mean percent error between the fluorometry and HPLC Chl a, with the logarithm of the ratio of Chl b: Chl a (Pearson's R: À0.051, pvalue = 0.2173, df = 579), and with the percent Chl b per Chls a + b (Pearson's R: 0.054, p-value = 0.1893, df = 579).

Total suspended solids mass and partitioning
Total suspended solids (TSS) measured gravimetrically on pre-weighed 47 mm Whatman GF/F filters after rinsing with distilled water. The organic fraction of TSS (OSPM) was determined as the weight lost by heating the filters for 3 h at 500 C (loss-on-ignition method), corrected by blank filters equally treated 47 samples had a OSPM slightly larger than TSS (a difference on the order of 0.1 mg in usually low weight samples with less than 1 mg L À1 ) and in these cases OSPM values were decreased to match TSS.

Phytoplankton taxonomy
Phytoplankton taxonomy was quantified following Utermohl's sedimentation method (Lund et al. 1958) with a Zeiss Axiovert 40 CFL inverted microscope at Â250 and Â500 magnifications. A minimum of 400 units were counted; these being single-celled individuals, filaments, or colonies depending on the organization of the algae. Weight biomass was calculated from recorded abundance and specific volume estimates, based on geometric solids (Rott 1981).

Laboratory measurement methodology and absorption coefficient calculation
Surface water was collected in dark containers at the deepest station of the lakes (664 lakes visited, depth ranging from $ 1 to more than 150 m and areas from $ 0.1 to 266 km 2 ) as part of the NSERC Canadian Lake Pulse Network field campaign (see Huot et al. 2019 for details on lake selection and NSERC Canadian Lake Pulse Network 2021 for the field sampling protocols) which occurred over three summers (2017, 2018, and 2019).
Collected water was filtered (two filter duplicates per water sample were analyzed for 101 lakes, one for all other lakes) in dim light in temporary (tents) laboratories on the lake's shore using 25 mm GF/F filters (Whatman). The filters were immediately stored at À80 C in individual plastic petri dishes. Volume to be filtered was determined from the Secchi depth (see Table 2; see Supporting Information Appendix S1 for effectiveness of the method) to obtain absorbance values that are within appropriate range (0.1-0.5) for the integrating sphere method (Röttgers and Gehnke 2012). Blank filters were also collected by filtering deionized water occasionally during the sampling campaign. Frozen samples were shipped on dry ice to the laboratory for analysis.
In the laboratory, filters were thawed under dim light at room temperature for 5 min and remoistened by placing filters on top of a drop of deionized water (MilliQ ® system) on aluminum covered petri dishes to minimize pigment degradation (Stramski 1990). The diameter of the filtration area was measured with a vernier caliper on select filters to ensure consistency (identical filtration kits were used for all filtration). Absorbance (A, unitless) scans from 800 to 300 nm (only the 800-400 nm range was kept for this study) were performed in a PerkinElmer's LAMBDA™ 650 UV/Vis spectrophotometer equipped with a 150-mm integrating sphere with a centermounted sample holder to obtain the total particle absorption spectra (a p ). New filters moistened with deionized water were used for the baseline and reference. After the scan, samples were transferred to filtration racks where they were washed by adding 5 mL of absolute methanol which was immediately pumped under low vacuum to remove moisture. Another 5 mL of methanol were added, and the filters were left to soak for 15 min for extraction (Kishino et al. 1985). After the extraction, the methanol was removed by pumping under low vacuum and rinsed with 15 mL of deionized water. Postextraction filters were scanned in the spectrophotometer. This measurement, after computation of the absorption coefficient and correction for pathlength amplification (see below), will provide the measurement of a E NAP . The filters were then bleached by putting a drop ($ 200 μL) of sodium hypochlorite (NaOCl, 1% active Cl) in a Petri dish and putting the filter on top (Tassan and Ferrari 1995) for 5 min. The filters were rinsed by setting them on top of a drop of deionized water. The filters were scanned again, which will provide a B NAP . At least 1 filter was measured from 649 lakes (out of the 664 sampled lakes), which, after including the 78 blanks and 106 duplicate samples, leads to a total of 835 filters analyzed (2505 spectra). The average absorbance of the field blanks of each treatment (untreated, post-extraction, and post-bleaching scans) was computed for each year (6 for 2017, 37 for 2018, and 37 for 2019). The mean blanks were subtracted from each filter scan of the corresponding treatment and year. Two corrections were then applied. First, if the average total particulate absorbance between 750 and 800 nm was negative, that average was subtracted at all wavelengths (10 total particulate filters, 17 post-extracted filters, and 47 post-bleaching filters). Methodologically, this can occur, for example, if the blank filters have higher absorbance compared to the filter used for the particulate filter: for the filters with mean negative nearinfrared absorption, the median value were À0.026, À0.057, and À0.016 for untreated, post-extracted, and post-bleached filters, respectively, while the blanks had a range of À0.002 to 0.019, À0.014 to 0.020, and À0.030 to 0.019, respectively. Drift might be behind the more negative values. Second, a pseudo-null point correction was performed by (1) computing the average A difference between the total particulate filter and the extracted filter between 750 and 800 nm (mean difference across all filters: À0.002 AE 0.007 absorption units for extraction) and (2) adding this difference to the extracted A spectra at all wavelengths. This correction assumes that all the 750 and 800 nm A is from the NAP fraction, making the A for the pigments fraction between 750 and 800 nm equal to 0 (Stramski et al. 2015). Methodologically, this can occur if the particles are not distributed homogeneously on the filters and the filter is rotated between the two measurements, if particles are displaced during the methanol extraction, or if by treating the filter, some particulate material was lost. The same correction was calculated for the bleaching method (mean difference: À0.012 AE 0.010 absorption units).
Absorption coefficients (a, m À1 ) were obtained from A using a ¼ 2:303 0:323 A 1:0867 where A is the absorbance of the filter; r f is filtration radius (m); and V f is the filtered volume (m 3 ). The coefficient 2.303 is the conversion factor from base 10 logarithm to the natural logarithm while the 0.323 coefficient and 1.0867 exponents are pathlength amplification correction coefficients for the integrating sphere method (Stramski et al. 2015). When the measured absorbance was below 0, at a given wavelength, the exponent of the correction was set to 1 instead of 1.0867 for that wavelength since elevating a negative number to a fraction is undefined in the set of real numbers.
Three absorption spectra are thus made directly with the spectrophotometer (see Fig. 1B, measurement column): the total particulate (a p ); the methanol extraction containing bleachable and non-bleachable non-algal colored material and unextracted pigments (a E NAP ); and the bleached filter which contains the non-bleachable colored material (a B NAP ). From these three basic measurements, three derived primary spectrum were calculated (Fig. 1B, "derived primary" column): (1) the "phytoplankton" absorption obtained from the methanol extraction NAP, a E φ = a pa E NAP ; (2) the "phytoplankton" absorption obtained from the bleached NAP a B φ = a pa B NAP ; and (3) remaining "bleachable material spectra" a U = a E NAPa B NAP , which represents the spectra of the non-extracted pigments and bleachable organic NAP matter. Note that we use quotation mark above when referring to phytoplankton absorption as neither is a good measure of the true phytoplankton in freshwaters as a E φ is missing unextracted pigments while a B φ includes the bleachable portion of the NAP.
Differential data processing Three different post-processing approaches were used to obtain the best a φ and a NAP . For the 1 st (V1), representing the traditional extraction used in oceanography, a φ was assumed equal to a E φ , and a NAP to a E NAP . For the 2 nd (V2), using the bleaching procedure, a φ was assumed equal to a B φ and a NAP to a B NAP , and the effects of the intermediate extraction were assumed to have a little impact in comparison to a direct bleaching. This assumption is supported by the equality of residual spectra obtained by both methods applied in parallel and sequentially in cultures without unextractable pigments (such as chromophyte algae) shown by Ferrari and Tassan (1999). A 3 rd method (V3), incorporating both extraction and bleaching with a series of numerical processing steps to account for the biases inherent to the treatments, was developed and the steps are described below.
The processing for the V3 method can be described as a series of four steps (numbers refer to the numbers on Fig. 1): 1. Compute a U by subtracting a B NAP from a E NAP , as described above. 2. Isolation of unextracted Chl a spectra. First, to remove the noise (which might heavily affect the next step), the a U spectra were passed through a Savitzky-Golay smoothing filter (Savitzky and Golay 1964, sgolayfilt in R library signal) with a bandwidth of 31 nm and using a 3 rd -degree polynomial function. Second, a continuum removal function (method of Clark and Roush 1984, as implemented in the continuum Removal function of the R package prospectr) was applied between 650 and 750 nm, and the resulting peak was retrieved. The shorter waveband at 650 nm was chosen to avoid the plateauing/downward part of the phycocyanin absorption peak at 620 nm. A pure Chl a (a Chla ) absorption spectra in methanol (Taniguchi and Lindsey 2021) was multiplied and shifted so the Chl a Qband peak (more precisely the Q y band, the red absorption peak of chlorophylls which in phytoplankton is almost entirely attributable to Chl a, Roesler and Barnard 2013) matches the absorption value and maximum wavelength of the retrieved peak, as: where a U Chla λ ð Þ is the unextracted Chl a spectra at wavelength λ; a Chla is the absorption of Chl a in methanol at wavelength λ shifted by the difference between the Q-band (longer wavelength) peak wavelength of the pure Chl a in methanol (λ Chla ¼ 666) and the unextracted bleached fraction Q-band estimated peak wavelength (λ U QÀband ); and a U QÀband is the Qband peak height of the same fraction. The resulting adjusted and wavelength-shifted Chl a was considered the unextracted Chl a spectrum (a U Chla ). If the maximum wavelength of the isolated peak was below 660 nm or above 700 nm, a U Chla was considered 0.
3. Isolation of unextracted phycocyanin spectra. The a U Chla were subtracted from a U . On the resulting spectra, a Savitzky-Golay smoothing filter (similar as in step 2) was applied, and a continuum removal function was applied between 750 and 450 nm, to isolate the unextracted phycobilins absorption (a U PB ).
Correction of a E NAP for unextracted pigments. The a U Chla and a U PB were subtracted from a E NAP to obtain the corrected a NAP , referred to as a Corr NAP . This a Corr NAP was then subtracted from a p spectra to obtain the a φ for the V3 method: a Corr φ . The three resulting a φ spectra were null-point corrected between 750 and 800 nm (near-infrared [NIR]), and this nullpoint absorption was added to the respective a NAP , since a φ does not have significant absorption in this range, and natural suspended particles have a NIR absorption of yet unknown source (Röttgers et al. 2014;Utschig and Röttgers 2020). For the 758 non-blank samples, the 750-800 nm mean values after blank removal were negative for only 8, 12, and 12 spectra for a p , a E NAP , and a B NAP , respectively. For around 80 a p measurements, NIR absorption were lower than the corresponding a E NAP . The choice of baseline addition instead of scaling the spectra is mentioned in the Supporting Information Appendix S1.

Quality control and outlier removal
A set of quality control tests were applied to flag bad spectra based on spectral shape properties and outlier tests based on other variables measured in LakePulse tied to equivalent IOPs.
Two specific absorptions were 1 st calculated. First, the Chl a-specific absorption coefficient (a * φ , in m 2 mg À1 ) was calculated as the a φ (mean when there were duplicates) divided by the Chl a concentration.
Second, the mean TSS (two duplicates) were used to calculate TSS-specific absorption coefficient of NAP (a * NAP (443) m 2 g À1 ), calculated as the mean lake a NAP divided by the TSS weight. Outlier tests were performed on a * NAP 443 ð Þ. Individual spectra were assigned with one or more of these six flags. Three flags relating to the shape of a φ specifically: (flag #1) a φ (676) being higher than a φ (443); (flag #2) a φ with substantial negative absorption (defined as > 10% of the maximum in the 400-700 nm range); and (flag #3) high NIR absorption in a φ (defined as a φ (790) > 1/3 a φ (676)). One flag (flag #4) duplicates with coefficient of variation > 50%. One flag (#5) testing for outliers using multiple criteria: 1.5 interquartile range, Rosner's test of multiple outliers (Rosner 1975), and absolute Z-score > 2 were performed on a * φ 443 ð Þ and a * φ 676 ð Þ, if any of these outlier tests was positive, flag#6 was added (3 for each a * φ wavelength) and the specific positive outlier tests were attached as comments for further consideration. The same three outlier tests of flag #5 were performed on a * NAP 443 ð Þas flag #7, and comments were added to the spectra. If a filter had two or more flags the data was discarded. If the filter had flag #4, and one of the duplicates had no other flags while the other had one or more, the bad duplicate was discarded. If the filters were flagged as outliers, but the duplicates were coincident (no flag 4) and no shape anomaly was flagged, the filters were kept. Only seven filters were discarded from further analysis, two of them had a duplicate that was kept. Four additional tests were applied directly to the postprocessed spectra with direct elimination: (1) to flag bad extractions, if the minimum value of a E φ in the range 650-400 nm was more negative than À0.1 * a E φ (676), the filter was eliminated (6 filters, 2 with a duplicate that was kept); (2) to eliminate bad extractions (loss of NAP material with the extraction), if the minimum value of a E φ in the range 650-400 nm was larger than 0.75 * a E φ (676), the filter was eliminated (4 filters); (3) to exclude filters where the filtered volume in the field was too high for pathlength correction, if the a p (620) multiplied by the filtered volume (in mL) was higher than 250, the filter was eliminated (1 filter). After eliminating the flagged spectra, we estimated the averages, standard deviations (SD), and the coefficient of variation (100*SD/mean) of the a NAP and a φ fractions for each lake when sample duplicates were measured, giving a total of 636 lake spectra.
The three methods for partitioning the absorption coefficient were evaluated by examining the relationship between the retrieved absorption coefficients by each method and variables such as Chl a concentration and TSS. To evaluate the changes in shape between treatments, two analyses were performed: First, the correlation between the organic fraction of suspended material (OSPM%) and S 400À700 NAP given that is has been shown that the slope increases with the proportion of organic particulate matter across coastal (Babin et al. 2003) and freshwaters (Riddick et al. 2015;Rodrigues et al. 2020;Shang et al. 2021), although in boreal lakes the relationship is either negative (Binding et al. 2008) or non-significant (Yacobi et al. 2015); while Babin et al. (2003) omitted the 400-480 and 620-710 nm ranges to diminish the effect of remaining pigments, we include those regions precisely to visualize said effects. Second, we analyzed the correlation between a φ 620 ð Þ=a φ 676 ð Þ ratio (indicator of phycocyanin per Chl a, Yacobi et al. 2015) and the cyanobacterial fraction of biovolume (CBV%), given that phycocyanin is well correlated with cyanobacterial biovolume (Randolph et al. 2008).

Assessment and results
The lakes studied had a mean Chl a concentration of 10.3 μg L À1 (range: 0-441.8 μg L À1 ), TSS of 12.3 mg L À1 (range: 0-3241.6 mg L À1 ), and a mean OPSM% of 66.4%. The mean a p (443) was 0.749 m À1 (range: 0.023-45.0 m À1 ; Fig. 2). The mean coefficient of variation for the 101 measured filter duplicates was 6.0% for a p , 7.7% for a E NAP , and 13.9% a B NAP , showing the fidelity of the sampling, filtration and measuring process. Biases in the extraction method and the bleaching method  appear as differences in the absorption spectral shapes and amplitude of the different methods. The presence of unextracted pigments is evident in many of the normalized a E NAP , where the phycocyanin and unextracted Chl a absorption signatures superpose onto the near exponential nature of a NAP (Fig. 3A). This is supported by a E φ (676) being on average 12.1% lower than a B φ (676) (Fig. 4B). However, part or all of the higher 676 nm absorption obtained by the bleaching procedure comes from the bleaching of non-algal organic material. The bleaching of organic non-algal material is evidenced by an 11.5% average decrease of a B NAP (443) relative to a E NAP (443) (Fig. 4A), or for a less phytoplankton impacted wavelength (560 nm) by an average reduction of a B NAP (560) of 22.1%, and by a 13.5% mean reduction of S 400À700 NAP (Fig. 4C) by bleaching relative to extraction. By analyzing a set of 3 filters with very low Chl a (< 1.0 μg L À1 ), where more than 90% of the absorption at 443 nm is attributable to NAP, we found that the reduction in absorption at 443 nm in comparison with a p was 6.2% for a E NAP , 19.3% for a B NAP , and 6.5% for a Corr NAP ; while the change in the 400-700 nm slope (in absolute value) in comparison to a p was 5.6% for a E NAP , 16.6% for a B NAP , and 7.9% for a Corr NAP . This demonstrates that the overcorrection of the bleaching step is recovered in the secondary processing steps (see Fig. 1).
Regarding the primary spectral differences between a E NAP and a B NAP , the a U spectra show a decreasing exponential with wavelength reflecting the oxidation of at least a fraction of the organic matter on which phycobilins and unextracted chlorophylls are superimposed (Fig. 5B). The ratio of the Q-band absorption between the unextracted and the extracted Chl a, a U Chla (669) : a Corr φ (676), ranged from 0 to 0.79 (mean AE SD = 0.044 AE 0.07, Fig. 5C). After the isolated unextracted Chl a was fitted, the remaining unextracted pigments (Fig. 5D), isolated by continuum removal, shows the shape and expected peaks of phycocyanins, with some rare cases where phycoerythrins might be the dominant phycobiliprotein (Ficek et al. 2004).
The new, combined method produces a NAP estimates that do not show the spectral signature of unextracted pigments (Fig. 3C), while keeping an almost unchanged amplitude with respect to a E NAP (443) by having a mean reduction of only 1.7% (7.4% for a E NAP [560]) in comparison to the extraction method (Fig. 4D). This reduction, although overall small, is higher than 0 due to the removal of unextracted Chl a, which for some filters reached more than 20% of the total unextracted 443 nm absorption (Fig. 4D). On the other hand, the distribution of the differences between a B φ (676) and a Corr φ (676) show a very high frequency of no difference (0%) but on average a Corr φ (676) was 5.9% smaller (Fig. 4E), showing the actual bleached organic non-algal material present in a B φ (676) since the continuum removal used to isolate the phycobilins isolates the pigment peaks found in that range and excludes the NAP background.
The differences in values among the three methods for a * φ (676) and a * NAP (443) were small in comparison with the variation between lakes and compared well with other studies, showing similar values to eutrophic lakes (Sun et al. 2010;Xue et al. 2017). The values were significantly larger than their marine (Bowers et al. 1996;Babin et al. 2003) counterparts or cultures of freshwater phytoplankton (Table 3).
Linear regressions between (1) the organic percentage of suspended solids (OSPM, %, Fig. 6, top row) and S 400À700 NAP ; and (2) between a φ 620 ð Þ=a φ 676 ð Þ and the cyanobacterial fraction of biovolume (CBV%, Fig. 6, bottom row) were fitted to check which method better reflects the lakes' physiochemistry and biology. For S 400À700 NAP and OSPM% it was found that, although overall they are poorly correlated, bleaching (R 2 = 0.111) and the new combined method (R 2 = 0.109) have a higher coefficient of determination than extraction (R 2 = 0.053), while for a φ 620 ð Þ=a φ 676 ð Þ and CBV%, extraction (R 2 = 0.333) and the new combined method (R 2 = 0.346) were better than bleaching (R 2 = 0.096). The root mean square error (RMSE) for fitted S 400À700 NAP vs. OSPM% and a φ 620 ð Þ=a φ 676 ð Þ vs. CBV% linear regressions, also supports this, with the new combined method having a lower RMSE than the other methods for OSPM% (RMSE = 0.00139), and slightly higher than extraction for CBV% (RMSE = 0.105 in comparison with extraction RSME, 0.093). These improvements, although mild (considering most spectra will not have significant differences across the three methods), support the idea that the combined methods have a strong specificity and produce spectral fractions that represent better the underlying water constituents especially when chlorophytes or cyanobacteria are dominant.

Discussion, comments, and recommendations
The issues of correct assignment of unextracted pigments to a φ and correct assignment of bleachable NAP to a NAP have been recognized in the literature (IOCCG Protocol Series 2018), but to our knowledge no practical methods were available. One solution for these issues was to fit an exponential function to a E NAP by excluding the spectral range where pigments are absorbing (i.e., 400-480 and 620-710 nm ranges; Babin et al. 2003). However, applying this method to our freshwater data produced 15 spectra with negative a φ 676 ð Þ and 120 spectra with negative a φ 620 ð Þ and therefore was not explored further. This is likely due to a higher complexity of a E NAP spectral shape in freshwaters (due to previously mentioned iron oxides and unextracted pigments) in comparison to marine equivalents.
The cut-offs used to estimate the filtered volume to obtain absorbances in the optimal range of the pathlength amplification correction (0.1-0.5; Röttgers and Gehnke 2012), were on average successful, with a new suggested category for Secchi depths < 1 m where the volume filtered should be 50 mL rather than 100 mL as adopted during LakePulse (see Supporting Information Appendix S1).
The presence of a chlorophyll Q-band is evident in the a E NAP and a U . On the development of the new method, we tried fitting a scaled and shifted version of a E φ , but it was producing overcorrection in the blue region. We found that the correction of unextracted chlorophylls by scaling and shifting a MeOH chlorophyll standard spectra is an empirical solution based on three main factors: (1) the observation of a Q-band peak shift on the unextracted chlorophylls, from a mean λ = 677.0 nm on the a φ spectra to a mean λ = 669.3 nm on the a U , between the peak of Chl a in a methanol solution (λ = 666 nm) and in a pyridine solution (λ = 671 nm, Table 3. Comparison of total suspended solids specific absorption coefficient a * NAP (443) (m 2 g À1 ) and the Chl a specific absorption coefficient a * φ (676) (m 2 mg À1 ) from this study and the literature. It includes the three methods of this work: non-algal particles absorption fraction by extraction (a E NAP , V1), bleaching (a B NAP , V2) and the new combined method (a Corr NAP , V3). Phytoplankton absorption fraction by extraction (a E φ , V1), bleaching (a B φ , V2), and the new combined method (a Corr φ , V3). For a NAP and TSS, values provided are from Giardino et al. (2017) and Mishra et al. (2017)    Taniguchi and Lindsey 2021); (2) the 2 nd -derivative spectra showing low to no spectral features of other pigments (Fig. 7); and (3) the absorption of NaOCl and bleached biomass in the 400-450 nm range (Ferrari and Tassan 1999) impedes the application of continuum removal functions to a U in that range. The application of such corrections on a U also avoids the interference of the continuum removal function on the $ 500 nm shoulder observed commonly on mineral NAP (Bowers and Binding 2006). The increase in S 400À700 NAP by using the bleaching process suggests that complex organic material, usually of higher absorption in the visible range and lower exponential slope (Uyguner and Bekbolet 2005;Binding et al. 2008;Helms et al. 2008), is oxidized by the bleaching process. The combination of extraction and bleaching could, in theory, be used to distinguish between organic and inorganic fractions of a E NAP ; however, in addition to the mentioned NaOCl treatment, the 400-450 nm absorption increase, the level of oxidation of non-algal matter attained by NaOCl is unknown, and therefore should remain as a supporting addition of the extraction method since the oxidation of pigments is known and certain. The retention of the shifted Q-band chlorophylls might be due to extraction resistance on some green algae (Shoaf and Lium 1976;Wood 1985;Ferrari and Tassan 1999;Wiltshire et al. 2000), likely by their cellulosealgaenan cell walls (Baudelet et al. 2017). The magnitude of the differences between spectra produced by the different methods justifies the application of the new corrections, as the cross-method error is larger than the duplicate error, and, for some samples, the difference between extraction and bleaching calculated fractions can be up to 100% of the smaller estimator. Since these differences are associated with high phycobilins and/or high bleachable non-algal material, which might indicate underlying human-induced impacts, obtaining the best possible separation will prevent misdiagnosis of lakes based on remote sensing reflectance. The proposed new method was shown to provide a more realistic fractioning both in shape and in magnitude, as supported by the higher correlation coefficient between the 400 and 700 nm log slope (S) of the non-algal particles' spectra and the organic fraction of the TSS, and by having a better correlation between the ratio between the absorption coefficient of phytoplankton at 620 and 676 nm and cyanobacterial biomass percentage (Fig. 6).
In terms of the logistical and laboratory complexity, this method requires one more filter measurement and 5 min of NaOCl bleaching over the methanol extraction method. This approach is faster than soaking the filters in methanol for a longer period of time to remove more pigments (Bélanger et al. 2013). Although we tested it on an integrating sphere configuration, other filter-pad measurement configurations (transmittance, transmittance-reflectance) will most likely produce similar results.
Overall, this method successfully solves two methodological problems: (1) unextracted pigments with methanol extraction methods and (2) the bleached fraction of the organic non-algal fraction, without introducing biases. Once this improved fractioning method is applied, a φ and a NAP exhibit more realistic relationships with other underlying measured biogeochemical properties.